मराठी

If (N + 1)! = 90 [(N − 1)!], Find N.

Advertisements
Advertisements

प्रश्न

If (n + 1)! = 90 [(n − 1)!], find n.

Advertisements

उत्तर

(n + 1)! = 90 [(n − 1)!]

\[\Rightarrow\](n + 1)\[\times\](n)\[\times\](n−1)! = 90[(n − 1)!]
\[\Rightarrow\](+ 1)\[\times\](n) = 90
\[\Rightarrow\](n + 1)\[\times\](n) = 10\[\times\] 9
On comparing, we get:
n = 9

 

shaalaa.com
Factorial N (N!) Permutations and Combinations
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 16: Permutations - Exercise 16.1 [पृष्ठ ४]

APPEARS IN

आर.डी. शर्मा Mathematics [English] Class 11
पाठ 16 Permutations
Exercise 16.1 | Q 8 | पृष्ठ ४

संबंधित प्रश्‍न

Convert the following products into factorials: 

3 · 6 · 9 · 12 · 15 · 18


Convert the following products into factorials: 

(n + 1) (n + 2) (n + 3) ... (2n)


If (n + 2)! = 60 [(n − 1)!], find n. 


Prove that:

\[\frac{(2n + 1)!}{n!}\] = 2n [1 · 3 · 5 ... (2n − 1) (2n + 1)]

If P (n, 4) = 12 . P (n, 2), find n.


If P (2n − 1, n) : P (2n + 1, n − 1) = 22 : 7 find n.


If P (n, 5) : P (n, 3) = 2 : 1, find n.


From among the 36 teachers in a school, one principal and one vice-principal are to be appointed. In how many ways can this be done?


How many words, with or without meaning, can be formed by using all the letters of the word 'DELHI', using each letter exactly once?


There are two works each of 3 volumes and two works each of 2 volumes; In how many ways can the 10 books be placed on a shelf so that the volumes of the same work are not separated?


How many 6-digit telephone numbers can be constructed with digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 if each number starts with 35 and no digit appears more than once?


Find the number of 4-digit numbers that can be formed using the digits 1, 2, 3, 4, 5, if no digit is repeated? How many of these will be even?


How many different words can be formed from the letters of the word 'GANESHPURI'? In how many of these words:

the letter G always occupies the first place?


How many permutations can be formed by the letters of the word, 'VOWELS', when

all vowels come together?


How many words can be formed out of the letters of the word 'ARTICLE', so that vowels occupy even places?


m men and n women are to be seated in a row so that no two women sit together. if m > n then show that the number of ways in which they can be seated as\[\frac{m! (m + 1)!}{(m - n + 1) !}\]


Find the number of words formed by permuting all the letters of the following words:
INDEPENDENCE


Find the number of words formed by permuting all the letters of the following words:
INTERMEDIATE


Find the number of words formed by permuting all the letters of the following words:
ARRANGE


Find the number of words formed by permuting all the letters of the following words:

RUSSIA


How many numbers can be formed with the digits 1, 2, 3, 4, 3, 2, 1 so that the odd digits always occupy the odd places?


How many number of four digits can be formed with the digits 1, 3, 3, 0?


How many different numbers, greater than 50000 can be formed with the digits 0, 1, 1, 5, 9.


How many permutations of the letters of the word 'MADHUBANI' do not begin with M but end with I?


Find the number of numbers, greater than a million, that can be formed with the digits 2, 3, 0, 3, 4, 2, 3.


How many numbers greater than 1000000 can be formed by using the digits 1, 2, 0, 2, 4, 2, 4?


In how many ways can the letters of the word ASSASSINATION be arranged so that all the S's are together?


If the letters of the word 'MOTHER' are written in all possible orders and these words are written out as in a dictionary, find the rank of the word 'MOTHER'.


If the permutations of a, b, c, d, e taken all together be written down in alphabetical order as in dictionary and numbered, find the rank of the permutation debac ?


In how many ways can the letters of the word "INTERMEDIATE" be arranged so that:

the relative order of vowels and consonants do not alter?


Prove that: 4nC2n : 2nCn = [1 · 3 · 5 ... (4n − 1)] : [1 · 3 · 5 ... (2n − 1)]2.


Let r and n be positive integers such that 1 ≤ r ≤ n. Then prove the following:
n · n − 1Cr − 1 = (n − r + 1) nCr − 1


Find the number of permutations of n different things taken r at a time such that two specified things occur together?


Write the expression nCr +1 + nCr − 1 + 2 × nCr in the simplest form.


Write the number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines.


Write the number of ways in which 12 boys may be divided into three groups of 4 boys each.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×